1 2 /* @(#)e_j0.c 5.1 93/09/24 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunPro, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 /* __ieee754_j0(x), __ieee754_y0(x) 15 * Bessel function of the first and second kinds of order zero. 16 * Method -- j0(x): 17 * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... 18 * 2. Reduce x to |x| since j0(x)=j0(-x), and 19 * for x in (0,2) 20 * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; 21 * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) 22 * for x in (2,inf) 23 * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) 24 * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) 25 * as follow: 26 * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) 27 * = 1/sqrt(2) * (cos(x) + sin(x)) 28 * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) 29 * = 1/sqrt(2) * (sin(x) - cos(x)) 30 * (To avoid cancellation, use 31 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 32 * to compute the worse one.) 33 * 34 * 3 Special cases 35 * j0(nan)= nan 36 * j0(0) = 1 37 * j0(inf) = 0 38 * 39 * Method -- y0(x): 40 * 1. For x<2. 41 * Since 42 * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) 43 * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. 44 * We use the following function to approximate y0, 45 * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 46 * where 47 * U(z) = u00 + u01*z + ... + u06*z^6 48 * V(z) = 1 + v01*z + ... + v04*z^4 49 * with absolute approximation error bounded by 2**-72. 50 * Note: For tiny x, U/V = u0 and j0(x)~1, hence 51 * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) 52 * 2. For x>=2. 53 * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) 54 * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) 55 * by the method mentioned above. 56 * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. 57 */ 58 59 #include "fdlibm.h" 60 61 #ifndef _DOUBLE_IS_32BITS 62 63 #ifdef __STDC__ 64 static double pzero(double), qzero(double); 65 #else 66 static double pzero(), qzero(); 67 #endif 68 69 #ifdef __STDC__ 70 static const double 71 #else 72 static double 73 #endif 74 huge = 1e300, 75 one = 1.0, 76 invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ 77 tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 78 /* R0/S0 on [0, 2.00] */ 79 R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ 80 R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ 81 R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ 82 R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */ 83 S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ 84 S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ 85 S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ 86 S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ 87 88 #ifdef __STDC__ 89 static const double zero = 0.0; 90 #else 91 static double zero = 0.0; 92 #endif 93 94 #ifdef __STDC__ __ieee754_j0(double x)95 double __ieee754_j0(double x) 96 #else 97 double __ieee754_j0(x) 98 double x; 99 #endif 100 { 101 double z, s,c,ss,cc,r,u,v; 102 __int32_t hx,ix; 103 104 GET_HIGH_WORD(hx,x); 105 ix = hx&0x7fffffff; 106 if(ix>=0x7ff00000) return one/(x*x); 107 x = fabs(x); 108 if(ix >= 0x40000000) { /* |x| >= 2.0 */ 109 s = sin(x); 110 c = cos(x); 111 ss = s-c; 112 cc = s+c; 113 if(ix<0x7fe00000) { /* make sure x+x not overflow */ 114 z = -cos(x+x); 115 if ((s*c)<zero) cc = z/ss; 116 else ss = z/cc; 117 } 118 /* 119 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) 120 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) 121 */ 122 if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(x); 123 else { 124 u = pzero(x); v = qzero(x); 125 z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(x); 126 } 127 return z; 128 } 129 if(ix<0x3f200000) { /* |x| < 2**-13 */ 130 if(huge+x>one) { /* raise inexact if x != 0 */ 131 if(ix<0x3e400000) return one; /* |x|<2**-27 */ 132 else return one - 0.25*x*x; 133 } 134 } 135 z = x*x; 136 r = z*(R02+z*(R03+z*(R04+z*R05))); 137 s = one+z*(S01+z*(S02+z*(S03+z*S04))); 138 if(ix < 0x3FF00000) { /* |x| < 1.00 */ 139 return one + z*(-0.25+(r/s)); 140 } else { 141 u = 0.5*x; 142 return((one+u)*(one-u)+z*(r/s)); 143 } 144 } 145 146 #ifdef __STDC__ 147 static const double 148 #else 149 static double 150 #endif 151 u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ 152 u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ 153 u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ 154 u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ 155 u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ 156 u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ 157 u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */ 158 v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ 159 v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ 160 v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ 161 v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ 162 163 #ifdef __STDC__ __ieee754_y0(double x)164 double __ieee754_y0(double x) 165 #else 166 double __ieee754_y0(x) 167 double x; 168 #endif 169 { 170 double z, s,c,ss,cc,u,v; 171 __int32_t hx,ix,lx; 172 173 EXTRACT_WORDS(hx,lx,x); 174 ix = 0x7fffffff&hx; 175 /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ 176 if(ix>=0x7ff00000) return one/(x+x*x); 177 if((ix|lx)==0) return -one/zero; 178 if(hx<0) return zero/zero; 179 if(ix >= 0x40000000) { /* |x| >= 2.0 */ 180 /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) 181 * where x0 = x-pi/4 182 * Better formula: 183 * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) 184 * = 1/sqrt(2) * (sin(x) + cos(x)) 185 * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) 186 * = 1/sqrt(2) * (sin(x) - cos(x)) 187 * To avoid cancellation, use 188 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 189 * to compute the worse one. 190 */ 191 s = sin(x); 192 c = cos(x); 193 ss = s-c; 194 cc = s+c; 195 /* 196 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) 197 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) 198 */ 199 if(ix<0x7fe00000) { /* make sure x+x not overflow */ 200 z = -cos(x+x); 201 if ((s*c)<zero) cc = z/ss; 202 else ss = z/cc; 203 } 204 if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x); 205 else { 206 u = pzero(x); v = qzero(x); 207 z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x); 208 } 209 return z; 210 } 211 if(ix<=0x3e400000) { /* x < 2**-27 */ 212 return(u00 + tpi*__ieee754_log(x)); 213 } 214 z = x*x; 215 u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); 216 v = one+z*(v01+z*(v02+z*(v03+z*v04))); 217 return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); 218 } 219 220 /* The asymptotic expansions of pzero is 221 * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. 222 * For x >= 2, We approximate pzero by 223 * pzero(x) = 1 + (R/S) 224 * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 225 * S = 1 + pS0*s^2 + ... + pS4*s^10 226 * and 227 * | pzero(x)-1-R/S | <= 2 ** ( -60.26) 228 */ 229 #ifdef __STDC__ 230 static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 231 #else 232 static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 233 #endif 234 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 235 -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ 236 -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ 237 -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ 238 -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ 239 -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ 240 }; 241 #ifdef __STDC__ 242 static const double pS8[5] = { 243 #else 244 static double pS8[5] = { 245 #endif 246 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ 247 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ 248 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ 249 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ 250 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ 251 }; 252 253 #ifdef __STDC__ 254 static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 255 #else 256 static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 257 #endif 258 -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ 259 -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ 260 -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ 261 -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ 262 -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ 263 -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ 264 }; 265 #ifdef __STDC__ 266 static const double pS5[5] = { 267 #else 268 static double pS5[5] = { 269 #endif 270 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ 271 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ 272 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ 273 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ 274 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ 275 }; 276 277 #ifdef __STDC__ 278 static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 279 #else 280 static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 281 #endif 282 -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ 283 -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ 284 -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ 285 -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ 286 -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ 287 -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ 288 }; 289 #ifdef __STDC__ 290 static const double pS3[5] = { 291 #else 292 static double pS3[5] = { 293 #endif 294 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ 295 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ 296 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ 297 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ 298 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ 299 }; 300 301 #ifdef __STDC__ 302 static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 303 #else 304 static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 305 #endif 306 -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ 307 -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ 308 -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ 309 -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ 310 -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ 311 -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ 312 }; 313 #ifdef __STDC__ 314 static const double pS2[5] = { 315 #else 316 static double pS2[5] = { 317 #endif 318 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ 319 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ 320 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ 321 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ 322 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ 323 }; 324 325 #ifdef __STDC__ pzero(double x)326 static double pzero(double x) 327 #else 328 static double pzero(x) 329 double x; 330 #endif 331 { 332 #ifdef __STDC__ 333 const double *p,*q; 334 #else 335 double *p,*q; 336 #endif 337 double z,r,s; 338 __int32_t ix; 339 GET_HIGH_WORD(ix,x); 340 ix &= 0x7fffffff; 341 if(ix>=0x40200000) {p = pR8; q= pS8;} 342 else if(ix>=0x40122E8B){p = pR5; q= pS5;} 343 else if(ix>=0x4006DB6D){p = pR3; q= pS3;} 344 else {p = pR2; q= pS2;} 345 z = one/(x*x); 346 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 347 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); 348 return one+ r/s; 349 } 350 351 352 /* For x >= 8, the asymptotic expansions of qzero is 353 * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. 354 * We approximate qzero by 355 * qzero(x) = s*(-1.25 + (R/S)) 356 * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 357 * S = 1 + qS0*s^2 + ... + qS5*s^12 358 * and 359 * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) 360 */ 361 #ifdef __STDC__ 362 static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 363 #else 364 static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 365 #endif 366 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 367 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ 368 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ 369 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ 370 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ 371 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ 372 }; 373 #ifdef __STDC__ 374 static const double qS8[6] = { 375 #else 376 static double qS8[6] = { 377 #endif 378 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ 379 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ 380 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ 381 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ 382 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ 383 -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ 384 }; 385 386 #ifdef __STDC__ 387 static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 388 #else 389 static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 390 #endif 391 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ 392 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ 393 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ 394 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ 395 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ 396 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ 397 }; 398 #ifdef __STDC__ 399 static const double qS5[6] = { 400 #else 401 static double qS5[6] = { 402 #endif 403 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ 404 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ 405 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ 406 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ 407 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ 408 -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ 409 }; 410 411 #ifdef __STDC__ 412 static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 413 #else 414 static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 415 #endif 416 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ 417 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ 418 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ 419 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ 420 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ 421 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ 422 }; 423 #ifdef __STDC__ 424 static const double qS3[6] = { 425 #else 426 static double qS3[6] = { 427 #endif 428 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ 429 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ 430 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ 431 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ 432 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ 433 -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ 434 }; 435 436 #ifdef __STDC__ 437 static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 438 #else 439 static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 440 #endif 441 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ 442 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ 443 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ 444 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ 445 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ 446 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ 447 }; 448 #ifdef __STDC__ 449 static const double qS2[6] = { 450 #else 451 static double qS2[6] = { 452 #endif 453 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ 454 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ 455 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ 456 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ 457 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ 458 -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ 459 }; 460 461 #ifdef __STDC__ qzero(double x)462 static double qzero(double x) 463 #else 464 static double qzero(x) 465 double x; 466 #endif 467 { 468 #ifdef __STDC__ 469 const double *p,*q; 470 #else 471 double *p,*q; 472 #endif 473 double s,r,z; 474 __int32_t ix; 475 GET_HIGH_WORD(ix,x); 476 ix &= 0x7fffffff; 477 if(ix>=0x40200000) {p = qR8; q= qS8;} 478 else if(ix>=0x40122E8B){p = qR5; q= qS5;} 479 else if(ix>=0x4006DB6D){p = qR3; q= qS3;} 480 else {p = qR2; q= qS2;} 481 z = one/(x*x); 482 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 483 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); 484 return (-.125 + r/s)/x; 485 } 486 487 #endif /* defined(_DOUBLE_IS_32BITS) */ 488